Five Classic Proofs without Words

In this video, we show animations of five famous/classic/iconic proofs without words: the formula for the sum of the first n integers; the formula for the difference of two squares; the formula for the sum of the first n odd integers; the pythagorean theorem using negative space/sliding rectangles/Chou pei suan ching; and the infinite geometric series of positive powers of 1/2 (using a rectangle/square dissection of a unit area square).

This is a longer version of this short:

For videos with related animations, see

#math #manim #pythagoreantheorem #pythagorean #triangle #animation #theorem #pww #proofwithoutwords #visualproof #proof #mathshorts #mathvideo #geometricseries #infiniteseries #finitesums #infinitesums #oddsumformula #sumsofintegers #sums #shorts

To learn more about animating with manim, check out:

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Music in this video:
Creative Commons / Attribution 4.0 International (CC BY 4.0)

[StudywithmeinPakistan]

I wish we had such animations in our time in 1999 when I was doing my engineering. Now adays education is becoming more easier than ever before.
Great channel.
Watching from Pakistan 🇵🇰.

[ZanderzMcCluer]

Beautiful. This video and this channel are amazing!

[shubhambawane]

Thank you for creating Visual videos of math

[anyoung]

This best channel in the multiverse!? 😮

[jakobthomsen]

Nice! Also in case you are looking for ideas for future videos: it seems you haven't animated the greatest common divisor algorithm yet. I think the GCD applied to a couple of examples would make a nice visualization.

[Atmatan]

Can you help me graph / animate a set i designed?
Also, maybe help point me to learning how to graph z transform fractal equations??
Im really struggling taking my work to its next level, entitely lacking a formal edication, and all..

[sugamonogaijin]

Really nice. May I ask what software do you use for these animations?

[RicardoGonzalez-tglw]

When I see these videos I can only think of how smart the guys that came up with these stuff were! And we're (most of us) now all just a bunch of idi0ts trying to understand it in the 21st century.

[academyofuselessideas]

Pretty cool... I have been wondering about the difference between verifying proofs and understanding them... These proofs can be done by algebraic methods (symbol-pushing) which is (arguably) the preferred method of standard mathematics/ But I wonder whether the symbol-pushing helps to understanding more than the geometric approach of this video. It is like the following Atiyah's quote:

Algebra is the offer made by the devil to the mathematician. The devil says: "I will give you this powerful machine, it will answer any question you like. All you need to do is give me your soul: give up geometry and you will have this marvellous machine." -Michael Atiyah

[ManishKashi]

Can you please share source code. And watching from India 😊